Image Denoising

In this module, we focus on the task of denoising an image. Techniques from the field of calculus of variations have recently been used to denoise images. Although the calculus of variations is not widely included in undergraduate courses, our materials are designed to let students explore and discover essential bits of the theory throughout an introductory real analysis course.

The .gif below depicts the iterative denoising process that students explore in the module. Notice that the flowers appear grainy at first, and successively the image is "smoothed."

.gif of a noisy image of purple flowers being denoised iteratively.

We have developed two versions of this module: The first (Abstract) is designed to be included in a single-semester real analysis course. The second (Abstract) includes material on the calculus of variations and is designed to be included in a two-semester real analysis sequence.

Please email us at to request a password to access our materials. All materials contain instructor notes and solutions. Therefore, we keep them password protected. Please do not share these materials. We are happy to give access to faculty who make a request.

One-Semester Course (Last Revised August 2022):

Two-Semester Course (Last Revised August 2022) :